1% test file for the Lie package
2
3% 1. n-dimensional Lie algebras with dimL1=1
4% n=6
5
6array lienstrucin(6,6,6)$
7
8lienstrucin(1,2,2):=lienstrucin(1,2,6):=lienstrucin(1,5,2):=-1$
9lienstrucin(1,5,6):=lienstrucin(2,5,3):=lienstrucin(2,5,5):=-1$
10lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=1$
11lienstrucin(1,5,5):=lienstrucin(2,5,2):=lienstrucin(2,5,6):=1$
12
13liendimcom1(6);
14
15% transformation matrix
16
17lientrans;
18
19clear lienstrucin$
20
21% n=8
22
23array lienstrucin(8,8,8)$
24
25lienstrucin(1,2,2):=lienstrucin(1,5,2):=lienstrucin(2,4,3):=1$
26lienstrucin(2,4,5):=lienstrucin(4,5,2):=1$
27lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=-1$
28lienstrucin(1,5,5):=lienstrucin(2,4,2):=lienstrucin(4,5,3):=-1$
29lienstrucin(4,5,5):=-1$
30lienstrucin(1,2,6):=lienstrucin(1,5,6):=lienstrucin(4,5,6):=5$
31lienstrucin(2,4,6):=-5$
32
33liendimcom1(8);
34
35% same with verbose output
36
37on tr_lie$
38
39liendimcom1(8);
40
41clear lienstrucin$
42
43off tr_lie$
44
45% 2. 4-dimensional Lie algebras
46
47% Korteweg-de Vries Equation: u_t+u_{xxx}+uu_x=0
48% symmetry algebra spanned by four vector fields:
49% v_1=d_x, v_2=d_t, v_3=td_x+d_u, v_4=xd_x+3td_t-2ud_u
50
51array liestrin(4,4,4)$
52
53liestrin(1,4,1):=liestrin(2,3,1):=1$
54liestrin(2,4,2):=3$
55liestrin(3,4,3):=-2$
56
57lieclass(4);
58
59clear liestrin$
60
61
62% dimL1=3, dimL2=3
63
64array liestrin(4,4,4)$
65
66liestrin(1,2,1):=-6$liestrin(1,2,3):=-2$liestrin(1,2,4):=6$
67liestrin(1,3,1):=-1$liestrin(1,3,2):=1$liestrin(1,3,4):=1$
68liestrin(2,3,1):=-3$liestrin(2,3,4):=2$
69liestrin(2,4,1):=6$liestrin(2,4,3):=2$liestrin(2,4,4):=-6$
70liestrin(3,4,1):=1$liestrin(3,4,2):=-1$liestrin(3,4,4):=-1$
71
72lieclass(4);
73
74% same with verbose output
75
76on tr_lie$
77
78lieclass(4);
79
80% transformation matrix
81
82liemat;
83
84clear liestrin$
85
86off tr_lie$
87
88
89end$
90
91
92